Sr Examen

Derivada de xxarctg4x

Función f() - derivada -er orden en el punto
v

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src]
x*x*atan(4*x)
$$x x \operatorname{atan}{\left(4 x \right)}$$
(x*x)*atan(4*x)
Gráfica
Primera derivada [src]
                      2  
                   4*x   
2*x*atan(4*x) + ---------
                        2
                1 + 16*x 
$$\frac{4 x^{2}}{16 x^{2} + 1} + 2 x \operatorname{atan}{\left(4 x \right)}$$
Segunda derivada [src]
  /         3                            \
  |     64*x           8*x               |
2*|- ------------ + --------- + atan(4*x)|
  |             2           2            |
  |  /        2\    1 + 16*x             |
  \  \1 + 16*x /                         /
$$2 \left(- \frac{64 x^{3}}{\left(16 x^{2} + 1\right)^{2}} + \frac{8 x}{16 x^{2} + 1} + \operatorname{atan}{\left(4 x \right)}\right)$$
Tercera derivada [src]
  /                      /           2  \\
  |                    2 |       64*x   ||
  |                16*x *|-1 + ---------||
  |          2           |             2||
  |      96*x            \     1 + 16*x /|
8*|3 - --------- + ----------------------|
  |            2                 2       |
  \    1 + 16*x          1 + 16*x        /
------------------------------------------
                        2                 
                1 + 16*x                  
$$\frac{8 \left(\frac{16 x^{2} \left(\frac{64 x^{2}}{16 x^{2} + 1} - 1\right)}{16 x^{2} + 1} - \frac{96 x^{2}}{16 x^{2} + 1} + 3\right)}{16 x^{2} + 1}$$
Gráfico
Derivada de xxarctg4x